tất cả các cách viết tắt các từ khi viết trong vở? ai biết tất cả mk tick cho , ví dụ như được là đc
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\(S=1\cdot2+2\cdot3+3\cdot4+...+2011\cdot2012\)
\(\Rightarrow3S=1\cdot2\cdot3+2\cdot3\cdot3+3\cdot4\cdot3+...+2011\cdot2012\cdot3\)
\(\Rightarrow3S=1\cdot2\cdot3+2\cdot3\cdot\left(4-1\right)+3\cdot4\cdot\left(5-2\right)+...+2011\cdot2012\cdot\left(2013-2010\right)\)
\(\Rightarrow3S=1\cdot2\cdot3+2\cdot3\cdot4-1\cdot2\cdot3+3\cdot4\cdot5-2\cdot3\cdot4+...+2011\cdot2012\cdot2013-2010\cdot20112012\)
\(\Rightarrow3S=2011\cdot2012\cdot2013\)
\(\Rightarrow S=\frac{2011\cdot2012\cdot2013}{3}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(0,5-\frac{2}{3}x=\frac{5}{12}\)
\(=\frac{1}{2}x=\frac{5}{12}+\frac{2}{3}\)
\(=\frac{1}{2}x=\frac{13}{12}\)
\(\Rightarrow x=\frac{13}{12}:\frac{1}{2}\)
\(\Rightarrow x=\frac{6}{13}\)
Vậy x = \(\frac{6}{13}\)
(#)
:3
![](https://rs.olm.vn/images/avt/0.png?1311)
Ta có :
\(\frac{4.5}{2.15}=\frac{2.1}{1.3}=\frac{2}{3}\)
Tham khảo nha !!!
![](https://rs.olm.vn/images/avt/0.png?1311)
Đặt \(A=4+2^2+2^3+2^4+...+2^{60}\)
\(A=2^2+2^2+2^3+...+2^{60}\)
\(2A=2^3+2^3+2^4+...+2^{61}\)
\(2A-A=\left(2^3+2^3+2^4+...+2^{61}\right)-\left(2^2+2^2+2^3+...+2^{60}\right)\)
\(A=2^3+2^{61}-2^2-2^2\)
\(A=2^3+2^{61}-2^2\left(1+1\right)\)
\(A=2^3+2^{61}-2^2.2\)
\(A=2^3+2^{61}-2^3\)
\(A=2^{61}\)
Vậy \(A=2^{61}\)
Chúc bạn học tốt ~
![](https://rs.olm.vn/images/avt/0.png?1311)
Gọi ƯCLN\(\left(2n+3;3n+7\right)=d\)
\(\Rightarrow\orbr{\begin{cases}2n+3⋮d\Rightarrow3.\left(2n+3\right)⋮d\Rightarrow6n+9⋮d\\3n+7⋮d\Rightarrow2.\left(3n+7\right)⋮d\Rightarrow6n+14⋮d̸\end{cases}}\)
\(\Rightarrow\left(6n+14\right)-\left(6n+9\right)⋮d\)
\(\Rightarrow5⋮d\Rightarrow d\in1;5\)
\(+d=5\Rightarrow6n+9⋮5\Rightarrow5n+\left(n+9\right)⋮5\)
\(\Rightarrow n+9⋮5\Rightarrow n+4⋮5\Rightarrow n=5k-4\)
Vậy n=5k-4 thì rút gọn đc
Vậy \(n\ne5k-4\Rightarrowđpcm\)
![](https://rs.olm.vn/images/avt/0.png?1311)
* Cách 1 :
Ta có :
\(16A=\frac{4^{17}+16}{4^{17}+1}=\frac{4^{17}+1+15}{4^{17}+1}=\frac{4^{17}+1}{4^{17}+1}+\frac{15}{4^{17}+1}=1+\frac{15}{4^{17}+1}\)
\(16B=\frac{4^{14}+16}{4^{14}+1}=\frac{4^{14}+1+15}{4^{14}+1}=\frac{4^{14}+1}{4^{14}+1}+\frac{15}{4^{14}+1}=1+\frac{15}{4^{14}+1}\)
Vì \(\frac{15}{4^{17}+1}< \frac{15}{4^{14}+1}\) nên \(1+\frac{15}{4^{17}+1}< 1+\frac{15}{4^{14}+1}\)
\(\Rightarrow\)\(16A< 16B\) hay \(A< B\)
Vậy \(A< B\)
Chúc bạn học tốt ~
\(4^2.A=\frac{4^2\left(4^{15}+1\right)}{4^{17}+1}\); \(4^2.B=\frac{4^2\left(4^{12}+1\right)}{4^{14}+1}\)
=> \(4^2.A=\frac{4^{17}+4^2}{4^{17}+1}\);\(4^2.B=\frac{4^{14}+4^2}{4^{14}+1}\)
=> \(4^2.A=\frac{4^{17}+1+4^2-1}{4^{17}+1}\); \(4^2.B=\frac{4^{14}+1+4^2-1}{4^{14}+1}\)
=> \(4^2.A=\frac{4^{17}+1}{4^{17}+1}+\frac{4^2-1}{4^{17}+1}\); \(4^2.B=\frac{4^{14}+1}{4^{14}+1}+\frac{4^2-1}{4^{14}+1}\)
=> \(4^2.A=1+\frac{4^2-1}{4^{17}+1}\); \(4^2.B=1+\frac{4^2-1}{4^{14}+1}\)
Mà \(4^{17}>4^{14}\)
=> \(4^{17}+1>4^{14}+1\)
=> \(\frac{4^2-1}{4^{17}+1}< \frac{4^2-1}{4^{14}+1}\)
=> \(1+\frac{4^2-1}{4^{17}+1}< 1+\frac{4^2-1}{4^{14}+1}\)
=> \(4^2.A< 4^2.B\)
=> \(A< B\)
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\frac{x-1}{2}=\frac{x+2}{4}\) <=> \(x-1=\frac{x+2}{2}\)
<=> 2x-2=x+2 <=> 2x-x=2+2 => x=4
Đáp số: x=4
\(=\frac{2\left(x-1\right)}{4}=\frac{x+2}{4}\)
\(=\frac{2\left(x-1\right)\cdot4}{4}=\frac{\left(x+2\right)\cdot4}{4}\)
\(=2\left(x-1\right)=x+2\)
\(=2x-2=x+2\)
\(=2x-x=2+2\)
\(=x=4\)
![](https://rs.olm.vn/images/avt/0.png?1311)
<=> 2xy-x=4y+4
<=> x(2y-1) = 4y+4 => \(x=\frac{4y+4}{2y-1}=\frac{4y-2+6}{2y-1}=\frac{2\left(2y-1\right)}{2y-1}+\frac{6}{2y-1}\)=> \(x=2+\frac{6}{2y-1}\)
Để x nguyên => 6 chia hết cho 2y-1 => 2y-1=(-6,-3,-2,-1,1,2,3,6) => y=(-5/2; -1; -1/2; 0; 1; 3/2; 2; 7/2)
Do y nguyên nên ta chọn được y=(-1, 0, 1, 2) => x=(0, -4, 8, 4)
Các cặp (x,y) thỏa mãn là: (0; -1), (-4,0); (8,1); (4,2)
- không là ko
- ừ là uk
- mình là mk
- thank you là tk
- bạn là bn
- câu lạc bộ là CLB
- ủy ban nhân dân là UBND
- trung học cơ sở là THCS
Ví dụ : nước là nc
Đang là dg , không là ko , ...